Martingales of Random Subsets of a Metric Space of Negative Curvature

We prove extension of classical convergence theorem of P. Lévy for martingales of random subsets of a metric space of negative curvature.     

Higgs boson production and weak boson structure

The influence of the QCD structure of the weak bosons on the Higgs boson production ine-p scattering is studied. The energy and Higgs boson mass dependence of the cross-section, following from the new contributions, is calculated. Work supported by the Polish State Committee for Scientifić Research (grant No. 2 P03B 081 09) and the Volkswagen-Stiftung     

Arbres de Markov Triplet et fusion de Dempster–Shafer

The hidden Markov chains (HMC) (X,Y) have been recently generalized to triplet Markov chains (TMC), which enjoy the same capabilities of restoring a hidden process X from the observed process Y. The posterior distribution of X can be viewed, in an HMC, as a particular case of the so called “Dempster–Shafer fusion” (DS fusion) of the prior Markov with a probability q defined from the observation Y=y. As such, when we place ourselves in the Dempster–Shafer theory of evidence by replacing the probability distribution of X by a mass function M having an analogous Markov form (which gives again the classical Markov probability distribution in a particular case), the result of DS fusion of M with q generalizes the conventional posterior distribution of X. Although this result is not necessarily a Markov distribution, it has been recently shown that it is a TMC, which renders traditional restoration methods applicable. The aim of this Note is to present some generalizations of the latter result: (i) more general HMCs can be considered; (ii) q, which can possibly be a mass function Q, is itself a result of the DS fusion; and (iii) all these results are finally specified in the hidden Markov trees (HMT) context, which generalizes the HMC one. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Homomo rphisms of the g roup $$L^1_s$$ into the g roup $$L^1_ r$$ fo r r ≤ 3

We determine all homomorphisms of the differential group L¹_sL^1_s with arbitrary s ≥ 2 into the group L¹_rL^1_r for r ≤  3.     

Quadratic harnesses, -commutations, and orthogonal martingale polynomials

We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a -commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest.

     

Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate

We discuss dynamics of a slow quantum phase transition in a spin-1 Bose-Einstein condensate. We analytically determine the scaling properties of the system magnetization and verify them with numerical simulations in a one dimensional model.     

Terahertz emission from collapsing field domains during switching of a gallium arsenide bipolar transistor

Broadband pulsed THz emission with peak power in the sub-mW range has been observed experimentally during avalanche switching in a gallium arsenide bipolar junction transistor at room temperature, while significantly higher total generated power is predicted in simulations. The emission is attributed to very fast oscillations in the conductivity current across the switching channels, which appear as a result of temporal evolution of the field domains generated in highly dense electron-hole plasma. This plasma is formed in turn by powerful impact ionization in multiple field domains of ultrahigh amplitude.